
"""simple docstring"""



from math import sqrt


def 			_UpperCamelCase						(    _A   )     ->	bool:





    """simple docstring"""

    assert isinstance(_A       ,   _A   ) and (
        number >= 0
    ), "'number' must been an int and positive"

    _UpperCAmelCase        = True

    # 0 and 1 are none primes.
    if number <= 1:
        _UpperCAmelCase        = False

    for divisor in range(2       ,   int(round(sqrt(_A   )   )   ) + 1   ):
        # if 'number' divisible by 'divisor' then sets 'status'
        # of false and break up the loop.
        if number % divisor == 0:
            _UpperCAmelCase        = False
            break

    # precondition
    assert isinstance(_A       ,   _A   ), "'status' must been from type bool"

    return status


def 			_UpperCamelCase						(    _A   )     ->	int:





    """simple docstring"""

    assert isinstance(_A       ,   _A   ) and (n > 2), "'N' must been an int and > 2"

    # beginList: contains all natural numbers from 2 up to N
    _UpperCAmelCase        = list(range(2       ,   n + 1   )   )

    _UpperCAmelCase        = []  # this list will be returns.

    # actual sieve of erathostenes
    for i in range(len(_A   )   ):
        for j in range(i + 1       ,   len(_A   )   ):
            if (begin_list[i] != 0) and (begin_list[j] % begin_list[i] == 0):
                _UpperCAmelCase        = 0

    # filters actual prime numbers.
    _UpperCAmelCase        = [x for x in begin_list if x != 0]

    # precondition
    assert isinstance(_A       ,   _A   ), "'ans' must been from type list"

    return ans


def 			_UpperCamelCase						(    _A   )     ->	Dict:





    """simple docstring"""

    assert isinstance(_A       ,   _A   ) and (n > 2), "'N' must been an int and > 2"

    _UpperCAmelCase        = []

    # iterates over all numbers between 2 up to N+1
    # if a number is prime then appends to list 'ans'
    for number in range(2       ,   n + 1   ):
        if is_prime(_A   ):
            ans.append(_A   )

    # precondition
    assert isinstance(_A       ,   _A   ), "'ans' must been from type list"

    return ans


def 			_UpperCamelCase						(    _A   )     ->	List[str]:





    """simple docstring"""

    assert isinstance(_A       ,   _A   ) and number >= 0, "'number' must been an int and >= 0"

    _UpperCAmelCase        = []  # this list will be returns of the function.

    # potential prime number factors.

    _UpperCAmelCase        = 2

    _UpperCAmelCase        = number

    if number == 0 or number == 1:
        ans.append(_A   )

    # if 'number' not prime then builds the prime factorization of 'number'
    elif not is_prime(_A   ):
        while quotient != 1:
            if is_prime(_A   ) and (quotient % factor == 0):
                ans.append(_A   )
                quotient /= factor
            else:
                factor += 1

    else:
        ans.append(_A   )

    # precondition
    assert isinstance(_A       ,   _A   ), "'ans' must been from type list"

    return ans


def 			_UpperCamelCase						(    _A   )     ->	Dict:





    """simple docstring"""

    assert isinstance(_A       ,   _A   ) and (
        number >= 0
    ), "'number' bust been an int and >= 0"

    _UpperCAmelCase        = 0

    # prime factorization of 'number'
    _UpperCAmelCase        = prime_factorization(_A   )

    _UpperCAmelCase        = max(_A   )

    # precondition
    assert isinstance(_A       ,   _A   ), "'ans' must been from type int"

    return ans


def 			_UpperCamelCase						(    _A   )     ->	str:





    """simple docstring"""

    assert isinstance(_A       ,   _A   ) and (
        number >= 0
    ), "'number' bust been an int and >= 0"

    _UpperCAmelCase        = 0

    # prime factorization of 'number'
    _UpperCAmelCase        = prime_factorization(_A   )

    _UpperCAmelCase        = min(_A   )

    # precondition
    assert isinstance(_A       ,   _A   ), "'ans' must been from type int"

    return ans


def 			_UpperCamelCase						(    _A   )     ->	Union[str, Any]:





    """simple docstring"""

    assert isinstance(_A       ,   _A   ), "'number' must been an int"
    assert isinstance(number % 2 == 0       ,   _A   ), "compare bust been from type bool"

    return number % 2 == 0


def 			_UpperCamelCase						(    _A   )     ->	Tuple:





    """simple docstring"""

    assert isinstance(_A       ,   _A   ), "'number' must been an int"
    assert isinstance(number % 2 != 0       ,   _A   ), "compare bust been from type bool"

    return number % 2 != 0


def 			_UpperCamelCase						(    _A   )     ->	List[str]:





    """simple docstring"""

    assert (
        isinstance(_A       ,   _A   ) and (number > 2) and is_even(_A   )
    ), "'number' must been an int, even and > 2"

    _UpperCAmelCase        = []  # this list will returned

    # creates a list of prime numbers between 2 up to 'number'
    _UpperCAmelCase        = get_prime_numbers(_A   )
    _UpperCAmelCase        = len(_A   )

    # run variable for while-loops.
    _UpperCAmelCase        = 0
    _UpperCAmelCase        = None

    # exit variable. for break up the loops
    _UpperCAmelCase        = True

    while i < len_pn and loop:
        _UpperCAmelCase        = i + 1

        while j < len_pn and loop:
            if prime_numbers[i] + prime_numbers[j] == number:
                _UpperCAmelCase        = False
                ans.append(prime_numbers[i]   )
                ans.append(prime_numbers[j]   )

            j += 1

        i += 1

    # precondition
    assert (
        isinstance(_A       ,   _A   )
        and (len(_A   ) == 2)
        and (ans[0] + ans[1] == number)
        and is_prime(ans[0]   )
        and is_prime(ans[1]   )
    ), "'ans' must contains two primes. And sum of elements must been eq 'number'"

    return ans


def 			_UpperCamelCase						(    _A       ,   _A   )     ->	List[str]:





    """simple docstring"""

    assert (
        isinstance(_A       ,   _A   )
        and isinstance(_A       ,   _A   )
        and (numbera >= 0)
        and (numbera >= 0)
    ), "'number1' and 'number2' must been positive integer."

    _UpperCAmelCase        = 0

    while numbera != 0:
        _UpperCAmelCase        = numbera % numbera
        _UpperCAmelCase        = numbera
        _UpperCAmelCase        = rest

    # precondition
    assert isinstance(_A       ,   _A   ) and (
        numbera >= 0
    ), "'number' must been from type int and positive"

    return numbera


def 			_UpperCamelCase						(    _A       ,   _A   )     ->	Union[str, Any]:





    """simple docstring"""

    assert (
        isinstance(_A       ,   _A   )
        and isinstance(_A       ,   _A   )
        and (numbera >= 1)
        and (numbera >= 1)
    ), "'number1' and 'number2' must been positive integer."

    _UpperCAmelCase        = 1  # actual answer that will be return.

    # for kgV (x,1)
    if numbera > 1 and numbera > 1:
        # builds the prime factorization of 'number1' and 'number2'
        _UpperCAmelCase        = prime_factorization(_A   )
        _UpperCAmelCase        = prime_factorization(_A   )

    elif numbera == 1 or numbera == 1:
        _UpperCAmelCase        = []
        _UpperCAmelCase        = []
        _UpperCAmelCase        = max(_A       ,   _A   )

    _UpperCAmelCase        = 0
    _UpperCAmelCase        = 0

    _UpperCAmelCase        = []  # captured numbers int both 'primeFac1' and 'primeFac2'

    # iterates through primeFac1
    for n in prime_fac_a:
        if n not in done:
            if n in prime_fac_a:
                _UpperCAmelCase        = prime_fac_a.count(_A   )
                _UpperCAmelCase        = prime_fac_a.count(_A   )

                for _ in range(max(_A       ,   _A   )   ):
                    ans *= n

            else:
                _UpperCAmelCase        = prime_fac_a.count(_A   )

                for _ in range(_A   ):
                    ans *= n

            done.append(_A   )

    # iterates through primeFac2
    for n in prime_fac_a:
        if n not in done:
            _UpperCAmelCase        = prime_fac_a.count(_A   )

            for _ in range(_A   ):
                ans *= n

            done.append(_A   )

    # precondition
    assert isinstance(_A       ,   _A   ) and (
        ans >= 0
    ), "'ans' must been from type int and positive"

    return ans


def 			_UpperCamelCase						(    _A   )     ->	List[str]:





    """simple docstring"""

    assert isinstance(_A       ,   _A   ) and (n >= 0), "'number' must been a positive int"

    _UpperCAmelCase        = 0
    _UpperCAmelCase        = 2  # this variable holds the answer

    while index < n:
        index += 1

        ans += 1  # counts to the next number

        # if ans not prime then
        # runs to the next prime number.
        while not is_prime(_A   ):
            ans += 1

    # precondition
    assert isinstance(_A       ,   _A   ) and is_prime(
        _A   ), "'ans' must been a prime number and from type int"

    return ans


def 			_UpperCamelCase						(    _A       ,   _A   )     ->	Any:





    """simple docstring"""

    assert (
        is_prime(_A   ) and is_prime(_A   ) and (p_number_a < p_number_a)
    ), "The arguments must been prime numbers and 'pNumber1' < 'pNumber2'"

    _UpperCAmelCase        = p_number_a + 1  # jump to the next number

    _UpperCAmelCase        = []  # this list will be returns.

    # if number is not prime then
    # fetch the next prime number.
    while not is_prime(_A   ):
        number += 1

    while number < p_number_a:
        ans.append(_A   )

        number += 1

        # fetch the next prime number.
        while not is_prime(_A   ):
            number += 1

    # precondition
    assert (
        isinstance(_A       ,   _A   )
        and ans[0] != p_number_a
        and ans[len(_A   ) - 1] != p_number_a
    ), "'ans' must been a list without the arguments"

    # 'ans' contains not 'pNumber1' and 'pNumber2' !
    return ans


def 			_UpperCamelCase						(    _A   )     ->	Dict:





    """simple docstring"""

    assert isinstance(_A       ,   _A   ) and (n >= 1), "'n' must been int and >= 1"

    _UpperCAmelCase        = []  # will be returned.

    for divisor in range(1       ,   n + 1   ):
        if n % divisor == 0:
            ans.append(_A   )

    # precondition
    assert ans[0] == 1 and ans[len(_A   ) - 1] == n, "Error in function getDivisiors(...)"

    return ans


def 			_UpperCamelCase						(    _A   )     ->	Tuple:





    """simple docstring"""

    assert isinstance(_A       ,   _A   ) and (
        number > 1
    ), "'number' must been an int and >= 1"

    _UpperCAmelCase        = get_divisors(_A   )

    # precondition
    assert (
        isinstance(_A       ,   _A   )
        and (divisors[0] == 1)
        and (divisors[len(_A   ) - 1] == number)
    ), "Error in help-function getDivisiors(...)"

    # summed all divisors up to 'number' (exclusive), hence [:-1]
    return sum(divisors[:-1]   ) == number


def 			_UpperCamelCase						(    _A       ,   _A   )     ->	Optional[int]:





    """simple docstring"""

    assert (
        isinstance(_A       ,   _A   )
        and isinstance(_A       ,   _A   )
        and (denominator != 0)
    ), "The arguments must been from type int and 'denominator' != 0"

    # build the greatest common divisor of numerator and denominator.
    _UpperCAmelCase        = gcd(abs(_A   )       ,   abs(_A   )   )

    # precondition
    assert (
        isinstance(_A       ,   _A   )
        and (numerator % gcd_of_fraction == 0)
        and (denominator % gcd_of_fraction == 0)
    ), "Error in function gcd(...,...)"

    return (numerator // gcd_of_fraction, denominator // gcd_of_fraction)


def 			_UpperCamelCase						(    _A   )     ->	Tuple:





    """simple docstring"""

    assert isinstance(_A       ,   _A   ) and (n >= 0), "'n' must been a int and >= 0"

    _UpperCAmelCase        = 1  # this will be return.

    for factor in range(1       ,   n + 1   ):
        ans *= factor

    return ans







def 			_UpperCamelCase						(    _A   )     ->	Union[str, Any]:





    """simple docstring"""

    assert isinstance(_A       ,   _A   ) and (n >= 0), "'n' must been an int and >= 0"

    _UpperCAmelCase        = 0
    _UpperCAmelCase        = 1
    _UpperCAmelCase        = 1  # this will be return

    for _ in range(n - 1   ):
        _UpperCAmelCase        = ans
        ans += fiba
        _UpperCAmelCase        = tmp

    return ans

"""simple docstring"""



import importlib
import os
from dataclasses import dataclass
from enum import Enum
from typing import Any, Dict, Optional, Union

import torch

from ..utils import BaseOutput


a       :						int       		=		'''scheduler_config.json'''




class 		a_    (			_UpperCAmelCase						):
    a   :					List[Any]			     =					1
    a   :					Tuple			     =					2
    a   :					Dict			     =					3
    a   :					str			     =					4
    a   :					Optional[int]			     =					5
    a   :					Any			     =					6
    a   :					int			     =					7
    a   :					Any			     =					8
    a   :					List[Any]			     =					9
    a   :					Any			     =					10
    a   :					List[str]			     =					11
    a   :					Optional[int]			     =					12
    a   :					Any			     =					13
    a   :					Dict			     =					14







@dataclass
class 		a_    (			_UpperCAmelCase						):
    a   :					torch.FloatTensor







class 		a_    :
    a   :					Dict			     =					SCHEDULER_CONFIG_NAME
    a   :					List[str]			     =					[]
    a   :					Optional[int]			     =					True







    @classmethod
    def   _snake_case       (      cls      :							List[str]  ,       __UpperCamelCase      :							Dict[str, Any] = None  ,       __UpperCamelCase      :							Optional[str] = None  ,       __UpperCamelCase      :							List[str]=False  ,       **__UpperCamelCase      :							int  ,       )		->Dict:






        '''simple docstring'''






        _UpperCAmelCase     ,_UpperCAmelCase     ,_UpperCAmelCase        = cls.load_config(
            pretrained_model_name_or_path=__UpperCamelCase  ,       subfolder=__UpperCamelCase  ,       return_unused_kwargs=__UpperCamelCase  ,       return_commit_hash=__UpperCamelCase  ,       **__UpperCamelCase  ,       )
        return cls.from_config(__UpperCamelCase  ,       return_unused_kwargs=__UpperCamelCase  ,       **__UpperCamelCase  )







    def   _snake_case       (      self      :							Tuple  ,       __UpperCamelCase      :							Union[str, os.PathLike]  ,       __UpperCamelCase      :							bool = False  ,       **__UpperCamelCase      :							List[str]  )		->Any:






        '''simple docstring'''






        self.save_config(save_directory=__UpperCamelCase  ,       push_to_hub=__UpperCamelCase  ,       **__UpperCamelCase  )







    @property
    def   _snake_case       (      self      :							Optional[int]  )		->List[Any]:






        '''simple docstring'''






        return self._get_compatibles()







    @classmethod
    def   _snake_case       (      cls      :							List[str]  )		->Dict:






        '''simple docstring'''






        _UpperCAmelCase        = list(set([cls.__name__] + cls._compatibles  )  )
        _UpperCAmelCase        = importlib.import_module(__name__.split("""."""  )[0]  )
        _UpperCAmelCase        = [
            getattr(__UpperCamelCase  ,       __UpperCamelCase  ) for c in compatible_classes_str if hasattr(__UpperCamelCase  ,       __UpperCamelCase  )
        ]
        return compatible_classes